As per Old-Biscuit's post it's going to depend on the controller for your charge solenoid, also known as isolation relay or aux start solenoid. Quick test is with a volt meter measuring battery voltage. When charging you'll see 13.2 VDC or more at a battery. When using the generator or shore power you would expect to see that level at the coach batteries and if the charge solenoid closes you'll find that level also at the chassis battery. Same for the engine alternator but chassis first then coach battery.
My Battery Control Center is the controller but will not tie the two batteries together until the primary battery (coach when using shore/battery power, chassis when the engine is running) until it senses a full charge. It will also disconnect the batteries if it senses a discharge to prevent both batteries from going flat. So it's possible yours could do the same.